The present invention relates to analysis of sensors and other structures, and more particularly, to methods, apparatus, and computer program products for determining structural motion.
Many sensor applications involve the detection of mechanical vibration or other motion. Examples of sensors that utilize such motion detection include Coriolis mass flowmeters and vibrating tube densitometers. These devices typically include a conduit or other vessel that is periodically driven, i.e., vibrated. Properties such as mass flow, density and the like associated with a material contained in the conduit or vessel may be determined by processing signals from motion transducers positioned on the containment structure, as the vibrational modes of the vibrating material-filled system generally are affected by the combined mass, stiffness and damping characteristics of the containing conduit or vessel structure and the material contained therein.
A typical Coriolis mass flowmeter includes one or more conduits that are connected inline in a pipeline or other transport system and convey material, e.g., fluids, slurries and the like, in the system. Each conduit may be viewed as having a set of natural vibrational modes including, for example, simple bending, torsional, radial and coupled modes. In a typical Coriolis mass flow measurement application, a conduit is excited at resonance in one of its natural vibrational modes as a material flows through the conduit, and motion of the conduit is measured at points along the conduit. Excitation is typically provided by an actuator, e.g., an electromechanical device, such as a voice coil-type driver, that perturbs the conduit in a periodic fashion. Exemplary Coriolis mass flowmeters are described in U.S. Pat. Nos. 4,109,524 to Smith, 4,491,025 to Smith et al., and Re. 31,450 to Smith.
Unfortunately, the accuracy of conventional Coriolis mass flowmeters may be compromised by nonlinearities and asymmetries in the conduit structure, motion arising from extraneous forces, such as forces generated by pumps and compressors that are attached to the flowmeter, and motion arising from pressure forces exerted by the material flowing through the flowmeter conduit. The effects of these forces are commonly reduced by using flowmeter designs that are balanced to reduce effects attributable to external vibration, and by using frequency domain filters, e.g., bandpass filters designed to filter out components of the motion signals away from the excitation frequency. However, mechanical filtering approaches are often limited by mechanical considerations, e.g., material limitations, mounting constraints, weight limitations, size limitations and the like, and frequency domain filtering may be ineffective at removing unwanted vibrational contributions near the excitation frequency.
According to embodiments of the invention, movement of a structure, such a conduit of a Coriolis mass flowmeter, is estimated. A plurality of motion signals representing motion of the structure are mode selective filtered to generate a plurality of mode selective filtered motion signals such that the mode selective filtered motion signals preferentially represent motion associated with a vibrational mode of the structure. A plurality of phase estimates is generated from the plurality of mode selective filtered motion signals. The plurality of phase estimates may be generated using a phase reference derived from a mode selective filtered motion signal of the plurality of mode selective filtered motion signals. According to some embodiments of the invention, the step of mode selective filtering includes the steps of applying a modal transformation to the plurality of motion signals to generate a plurality of modal motion signals in a modal coordinate domain and applying a mode selective transformation to the plurality of modal motion signals to generate the plurality of mode selective filtered motion signals.
According to other embodiments of the invention, a frequency of a mode selective filtered motion signal of the plurality of mode selective filtered motion signals is estimated. Quadrature first and second reference signals based on the estimated frequency. The plurality of phase estimates is generated from the plurality of mode selective filtered motion signals and the first and second reference signals. For example, a mode selective filtered motion signal is multiplied by respective ones of the first and second reference signals to generate respective real and imaginary component signals of the mode selective filtered motion signal. An arctangent of a quotient of the real and imaginary component signals of the mode selective filtered motion signal is determined to generate a phase estimate.
According to still other embodiments, a plurality of time difference estimates is generated from the plurality of phase estimates. For example, the plurality of phase estimates may be divided by a mode frequency to generate the plurality of time difference estimates. The mode frequency may be determined by applying a modal transformation to the plurality of motion signals to generate a modal motion signal in a modal coordinate domain, and estimating the mode frequency from the modal motion signal.
According to still other embodiments, an intercept parameter of a scaling function that relates the plurality of time difference estimates to a plurality of reference time differences representing motion of the structure under a known perturbation is estimated. A system status is determined from the intercept parameter. For example, an augmented matrix including the plurality of reference time differences may be generated. The plurality of time difference estimates may be multiplied by a pseudoinverse of the augmented matrix to estimate the intercept parameter. Alternatively, the scaling function may be iteratively estimated, e.g., using a least mean square (LMS) estimation procedure.
According to other aspects of the invention, a plurality of motion signals representing motion of the structure are mode selective filtered to generate a plurality of mode selective filtered motion signals such that the plurality of mode selective filtered motion signals preferentially represents motion associated with a vibrational mode of the structure. A frequency of a first mode selective filtered motion signal of the plurality of mode selective filtered motion signals is estimated. A difference estimate is then generated from a second mode selective filtered motion signal of the plurality of mode selective filtered motion signals and the estimated frequency.
According to still other aspects of the invention, a system including a structure is monitored by processing a plurality of motion signals representing motion of the structure to generate a plurality of difference estimates. A correlation measure is generated from the plurality of time difference estimates. A system status is then determined from the correlation measure. For example, the step of generating a correlation measure may include the step of estimating an intercept parameter of a scaling function that relates the plurality of difference estimates to a plurality of reference differences representing motion of the structure under a known perturbation.
According to other embodiments, an apparatus includes a mode selective filter that filters a plurality of motion signals representing motion of a structure to generate a plurality of mode selective filtered motion signals such that the mode selective filtered motion signals preferentially represent motion associated with a vibrational mode of the structure. A phase estimator generates a plurality of phase estimates from the plurality of mode selective filtered motion signals. The phase estimator may generate the plurality of phase estimates using a phase reference derived from a mode selective filtered motion signal of the plurality of mode selective filtered motion signals.
According to still other embodiments, an apparatus for monitoring a system including a structure includes means for processing a plurality of motion signals representing motion of the structure to generate a plurality of difference estimates. Means are provided for generating a correlation measure from the plurality of time difference estimates. Means are also provided for determining a system status from the correlation measure.
According to other embodiments of the invention, a computer program product for estimating movement of a structure is provided. The computer program product includes a computer-readable storage medium having computer-readable program code embodied in the computer-readable storage medium. The computer-readable program code includes first computer-readable program code that mode selective filters a plurality of motion signals representing motion of the structure to generate a plurality of mode selective filtered motion signals such that the mode selective filtered motion signals preferentially represent motion associated with a vibrational mode of the structure, and that generates a plurality of phase estimates from the plurality of mode selective filtered motion signals. The first computer-readable program code may generate the plurality of phase estimates using a phase reference derived from a mode selective filtered motion signal of the plurality of mode selective filtered motion signals.